DSi mode is exactly what it sounds like. The DSi uses a different mode than the DS and has access to the various other features that the DSi has, such as the camera, the SD slot, and the hardware. Of course, this is only for the DSi (because obviously the DS doesn't have a variety of the extra stuff added to the DSi). This plays into buying a flashcart if you are a homebrew goer or if you want to place your hopes in having support for commercial DSi-enhanced games...and maybe DSi games in the far far future.
In terms of homebrew, there could be the possibility of homebrew utilizing the camera, the SD slot, etc. in the future and there isn't that much regression with the compatibility layer already added (though the compatibility layer...